Page 164 - Sensing, Intelligence, Motion : How Robots and Humans Move in an Unstructured World

CHAPTER 4

Accounting for Body Dynamics:
The Jogger’s Problem

Let me first explain to you how the motions of different kinds of matter depend
on a property called inertia.
—Sir William Thomson (Lord Kelvin), The Tides

4.1 PROBLEM STATEMENT

As discussed before, motion planning algorithms usually adhere to one of the
two paradigms that differ primarily by their assumptions about input informa-
tion: motion planning with complete information (Piano Mover’s problem)and
motion planning with incomplete information (sensor-based motion planning, SIM
paradigm, see Chapter 1). Strategies that come out of the two paradigms can be
also classified into two groups: kinematic approaches, which consider only kine-
matic and geometric issues, and dynamic approaches, which take into account
the system dynamics. This classification is independent from the classification
into the two paradigms. In Chapter 3 we studied kinematic sensor-based motion
planning algorithms. In this chapter we will study dynamic sensor-based motion
planning algorithms.
What is so dynamic about dynamic approaches? In strategies that we consid-
ered in Chapter 3, it was implicitly assumed that whatever direction of motion
is good for the robot’s next step from the standpoint of its goal, the robot will
be able to accomplish it. If this is true, in the terminology of control theory such
a system is called a holonomic system [78]. In a holonomic system the number
of control variables available is no less that the problem dimensionality. The
system will also work as intended in situations where the above condition is not
satisfied, but for some reason the robot dynamics can be ignored. For example,
a very slowly moving robot can turn on a dime and hence can execute any sharp
turn if prescribed by its motion planning software.
Most of existing approaches to motion planning (including those within the
Piano Mover’s model) assume, first, that the system is holonomic and, second,
Sensing, Intelligence, Motion, by Vladimir J. Lumelsky
Copyright  2006 John Wiley & Sons, Inc.
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